A method for data storage includes defining an end-to-end mapping between data bits to be stored in a memory device that includes multiple memory cells and predefined programming levels. The data bits are mapped into mapped bits, so that the number of the mapped bits is smaller than the number of the data bits. The data bits are stored in the memory device by programming the mapped bits in the memory cells using a programming scheme that guarantees the end-to-end mapping. After storing the data bits, the data bits are read from the memory device in accordance with the end-to-end mapping.